A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range

Abstract

A so called staggered precision arithmetic is a special kind of
a multiple precision arithmetic based on the underlying
floating point data format (typically IEEE double format)
and fast floating point operations as well as exact dot product computations.
Due to floating point limitations it is not an arbitrary precision arithmetic.
However, it typically allows computations using several hundred mantissa digits.
A set of new modified staggered arithmetics for real and
complex data as well as for real interval and
complex interval data with very wide exponent range is presented.
Some applications show
the increased accuracy of computed results compared to ordinary staggered
interval computations. The very wide exponent range of the new arithmetic
operations allows computations far beyond the IEEE data formats.
The new arithmetics would be extremly fast, if an exact dot product was
available in hardware (the fused accumulate and add instruction is only
one step in this direction).